Chaos and Lévy flights in the three-body problem

Author:

Manwadkar Viraj12ORCID,Trani Alessandro A3,Leigh Nathan W C24

Affiliation:

1. Department of Astronomy and Astrophysics, University of Chicago, 5640 S. Ellis Ave., Chicago, IL 60637, USA

2. Departamento de Astronomía, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Concepción 4030000, Chile

3. Department of Astronomy, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

4. Department of Astrophysics, American Museum of Natural History, Central Park West and 79th Street, New York, NY 10024, USA

Abstract

ABSTRACT We study chaos and Lévy flights in the general gravitational three-body problem. We introduce new metrics to characterize the time evolution and final lifetime distributions, namely Scramble Density $\mathcal {S}$ and the Lévy flight (LF) index $\mathcal {L}$, that are derived from the Agekyan–Anosova maps and homology radius $R_{\mathcal {H}}$. Based on these metrics, we develop detailed procedures to isolate the ergodic interactions and Lévy flight interactions. This enables us to study the three-body lifetime distribution in more detail by decomposing it into the individual distributions from the different kinds of interactions. We observe that ergodic interactions follow an exponential decay distribution similar to that of radioactive decay. Meanwhile, Lévy flight interactions follow a power-law distribution. Lévy flights in fact dominate the tail of the general three-body lifetime distribution, providing conclusive evidence for the speculated connection between power-law tails and Lévy flight interactions. We propose a new physically motivated model for the lifetime distribution of three-body systems and discuss how it can be used to extract information about the underlying ergodic and Lévy flight interactions. We discuss ejection probabilities in three-body systems in the ergodic limit and compare it to previous ergodic formalisms. We introduce a novel mechanism for a three-body relaxation process and discuss its relevance in general three-body systems.

Funder

Fondo Nacional de Desarrollo Científico y Tecnológico

George Cedric Metcalf Charitable Foundation

Japan Society for the Promotion of Science

Publisher

Oxford University Press (OUP)

Subject

Space and Planetary Science,Astronomy and Astrophysics

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